The Annals of Mathematical Statistics

Consistency and Unbiasedness of Certain Nonparametric Tests

E. L. Lehmann

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Abstract

It is shown that there exist strictly unbiased and consistent tests for the univariate and multivariate two- and $k$-sample problem, for the hypothesis of independence, and for the hypothesis of symmetry with respect to a given point. Certain new tests for the univariate two-sample problem are discussed. The large sample power of these tests and of the Mann-Whitney test are obtained by means of a theorem of Hoeffding. There is a discussion of the problem of tied observations.

Article information

Source
Ann. Math. Statist., Volume 22, Number 2 (1951), 165-179.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177729639

Digital Object Identifier
doi:10.1214/aoms/1177729639

Mathematical Reviews number (MathSciNet)
MR40632

Zentralblatt MATH identifier
0045.40903

JSTOR
links.jstor.org

Citation

Lehmann, E. L. Consistency and Unbiasedness of Certain Nonparametric Tests. Ann. Math. Statist. 22 (1951), no. 2, 165--179. doi:10.1214/aoms/1177729639. https://projecteuclid.org/euclid.aoms/1177729639


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